Several people have argued that Rabbi Mizrachi is surely no innovator in this regard (and he himself claims that what he said is "in every Gemara"). Consider the words of Prof. Haym Soloveitchik in his seminal essay Rupture and Reconstruction:
Rabbi Isaac Peretz, a Sefaredi haredi and Israeli minister of interior, stated that the seventeen children and five adults killed when a train ran over their school bus died because of the recent public desecration of Sabbath in Petah Tikvah. These remarks caused a furor in the general community... Rabbi Peretz's remarks simply expressed the classic religious explanation of linking misfortune with guilt (pishpush be ma'asim), which would have been uttered by any preacher of the past millennium. Indeed, R. Nissim Yagen, the Sefaredi preacher, brought further proof of the causal link, as would have preachers of the past by pointing out a number of correlations: first, that the number of the dead totaled twenty two, which was also the date of the public opening of the movie theaters in Petah Tikvah (22 Sivan); second, the sum total of the dead and wounded amounted to thirty nine, which corresponds to the number of types of work forbidden on the Sabbath (lamed-tet avot melakhot). As noted above, the Sefaredic world has encountered modernity only recently, and in many ways, as in the palpable sense of the rewards and terrors of the afterlife and of God's immediate involvement in human affairs, remains far closer to the religious sensibilities of their fathers than does the more unconsciously acculturated members of the Ashkenazic community.Indeed, Rav Ovadia Yosef made similarly shocking statements about the victims of the Holocaust, the victims of Hurricane Katrina, and so on, and you don't see a hexadecarabbinical (HDR) condemnation of him. Going a little further back, there is no shortage of prestigious rabbis blaming the Holocaust on various sins, be it Zionism or assimilation. Even further back, Rabbi Yom Tov Lipmann Heller (the Tosafos Yom Tov) attributed the horrific Chmielnicki massacres to people talking in shul. And in the Gemara itself we find the Churban blamed on various sins. Surely, then, Rabbi Mizrachi is following in Torah tradition?
There is a lot to be said in response to this, and not all of it is pretty. Nor is this quite the right forum to do justice to such a complicated topic. However, let me at least sketch some basic points.
First of all, it is clear that nobody knows why things happen. Unless you receive a Divine prophecy from God Himself, there is simply no way to ever ultimately know why things happen. And rabbinic sages are not prophets. Note that even Chazal do not give a single definitive statement as to why the Churban happened; several different views are stated. Whatever insight Chazal had, it was not prophetic, and thus there could be no definitive, unequivocal explanation. In fact, the most traditional response to suffering is to simply confess ignorance. We have an entire book of Tanach on this topic: the Book of Iyov. And God's response to Iyov's suffering, to his having lost his children, is not to explain that his children watched pornography in a previous life. Rather, it is that Iyov, as a mortal, cannot expect to understand God's ways. Likewise, Chazal tell us how Moshe Rabbeinu posed the ultimate question of why bad things happen to good people, and he wasn't told that it was because there were women wearing long sheitels. Yet here comes Rabbi Mizrachi and claims that it's all so simple! That is not the traditional Torah approach.
Second, and this is the most crucial point, even if one's views regarding theodicy are correct, it can still be a sin to state them. There is a prohibition in the Torah of Lo sonu ish es amiso, "Do not oppress one another" (Vayikra 25:17). The Gemara in Bava Metzia 58b elaborates upon the sin of ona'as devarim, oppressing someone with words. One of the examples given is that if someone is suffering, it is forbidden to tell them that this is because they have sinned. Now, it is clear that Chazal held that this may indeed be the reason why the person is suffering; yet it is a sin to tell that to the person! Speculating as to the sins that led to tragedy must be done with great care. It can be a powerful tool to spur people to improve their ways. However, it can also involve a terrible transgression of ona'as devarim. It takes great wisdom and sensitivity to know when it is appropriate to issue such speculations, and how to issue them. To post a video on YouTube, and to glibly, smilingly talk about how child suffering is the result of their sins such as watching porn in a previous life, and how one shouldn't say "poor child!", is not traditional talk about theodicy; it is supremely sinful idiocy.
But don't some of Rav Ovadyah Yosef's statements fall into the same category? Yes, they do. And it should not have been left to Meretz MKs to call him out on such things. Still, there is enough other substance in Rav Ovadyah Yosef's career to understand how he managed to escape an HDR condemnation. With Rabbi Mizrachi, on the other hand, after you dismiss his arrogant and ridiculous claims of having made 150,00 people religious and having created "the most successful kiruv system in the world and perhaps in history," you get a charismatic but boorish entertainer with little scholarship or substance, possessing poor character traits of arrogance and dishonesty, who excels in attracting unsavory types, who responds with appalling viciousness to those that are understandably offended by his talks, who inspires people to make a religion out of offensive attitudes, and who manages to aggregate the most irrational and offensive claims in the history of rabbinic literature and apply them in such a way as to make them even more irrational and offensive. There's just not enough of value to get him off the hook.
(It was also pointed out to me that with the exception of Rav Ovadya, the others flew below the radar of the general community. They did not create massive chilul Hashem, or cause people to walk out of Yiddishkeit, as Rabbi Mizrachi has done. Furthermore, Rav Ovadya could count on the majority of those in the room with him to take his remarks as hyperbolic drama, rather than literally, even if that could not be said about everyone who would later hear the recordings. Rabbi Mizrachi, on the other hand, appears to specifically aim to be taken literally.)
Yasher koach to the signatories of the HDR, and let us wish them strength in the face of the nasty attacks of Rabbi Mizrachi and his devotees. And may we all try to increase our wisdom and sensitivity.